Pith Number

pith:AKBRRNCD

pith:2014:AKBRRNCDR4VBKNUGQO3UYFY6UE

not attested not anchored not stored refs pending

On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

Andrew V. Sutherland, Igor E. Shparlinski

arxiv:1404.0399 v3 · 2014-04-01 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AKBRRNCDR4VBKNUGQO3UYFY6UE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:53:34.969161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

028318b4438f2a15368683b74c171ea1145bb9dacecb243ca5c011dbcd860878

Aliases

arxiv: 1404.0399 · arxiv_version: 1404.0399v3 · doi: 10.48550/arxiv.1404.0399 · pith_short_12: AKBRRNCDR4VB · pith_short_16: AKBRRNCDR4VBKNUG · pith_short_8: AKBRRNCD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AKBRRNCDR4VBKNUGQO3UYFY6UE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 028318b4438f2a15368683b74c171ea1145bb9dacecb243ca5c011dbcd860878

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9f58b2d16074d702f9f85748ceaae30e5dbf7f7bcf6f90a8e046bc2c1a3be1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-04-01T21:11:30Z",
    "title_canon_sha256": "ee4585fae87c9c0cdba11e37cecb45257303bda7e5ef6f27e4cd647e1392ebe8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.0399",
    "kind": "arxiv",
    "version": 3
  }
}